On Pointwise Gradient Estimates for the Complex Monge-Ampere Equation

TL;DR

This paper introduces a new pointwise gradient estimate for the complex Monge-Ampere equation that depends solely on the infimum of the solution, improving upon previous estimates that relied on the $C^0$ norm.

Contribution

It presents a novel pointwise gradient estimate for the complex Monge-Ampere equation that depends only on the infimum of the solution, unlike prior estimates.

Findings

Established a pointwise gradient estimate for the complex Monge-Ampere equation.

The estimate depends only on the infimum of the solution, not its $C^0$ norm.

Improves upon previous estimates by Yau, Hanani, Blocki, Guan, and Li.

Abstract

In this note, a gradient estimate for the complex Monge-Ampere equation is established. It differs from previous estimates of Yau, Hanani, Blocki, P. Guan, B. Guan - Q. Li in that it is pointwise, and depends only on the infimum of the solution instead of its $C^0$ norm.